\subsection{Analyzing the Data}
As mentioned, the participants were tested both with and without a reference paper. When looking at the data, there are only minor differences between the results with and without the papers. Because of this, it has been chosen to only look at the data without the reference paper, to make data analysis simpler.

The test participants were asked to rate themselves via several statements. Their answers covered the four different criteria mentioned in Section \ref{VibrationCrit}, based on a Likert scale from 1-5 \citep{InteractDesign}, where 1 is \textit{Strongly disagree} and 5 is \textit{Strongly agree}.

Note that all graphs in the following are based on averages.

\subsubsection{Reaction Times}
The test participants' reaction times were logged for all five different vibration patterns. Each of the vibrations had a certain duration (see Figure \ref{fig:TableOVibrationfDuration}). Even though it was possible for the participants to press a button before the vibration ended, it has been chosen to subtract the vibration durations from the reaction times. An example could be the \textit{static intensity} pattern that lasts for 2 seconds: if a test participant waits for the full duration of the vibration, and then presses the button after a total of 3 seconds, his reaction time would be $3-2$ seconds $=$ 1 second.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/TableOVibrationfDuration}
\caption{The duration of the five vibrations, which are then subtracted from the logged reaction times.}
\label{fig:TableOVibrationfDuration}
\end{figure}

Figure \ref{fig:ReactionTimeMinusRumbleDuration} illustrates how much time lasts from the moment that the vibration stops to the point where the participants react. For instance, it can be seen that the participants spent approximately 1.2 seconds to react to the \textit{varying intensity} pattern, while they only spent 0.1 seconds to react to the \textit{interval} pattern. Also, it should be noted that the \textit{right-left} reaction times are negative. This happened because the test participants, in average, pressed one of the buttons \textit{before} the vibrations ended.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/ReactionTimeMinusRumbleDuration}
\caption{Reaction times in seconds, minus the vibration durations. The reaction time of \textit{right-left} is negative due to fact of the test participants pressed one of the buttons before the vibration ended.}
\label{fig:ReactionTimeMinusRumbleDuration}
\end{figure}

Figure \ref{fig:ReactionTimeMinusRumbleDuration} further shows that the data follows the Hick-Hyman law mentioned in Section \ref{Theory}: that the rate of gain of information  has a linear relationship with time. Put differently, the more information held in each of the vibration patterns, the longer the reaction times seem to be. E.g\ the \textit{interval} pattern holds discrete information (full power with a small pause, either one, two, three of four times), while the \textit{varying intensity} pattern holds continuous information in the form of gradually increasing/decreasing the vibration's power. The first clearly has faster reaction times than the latter.

Also, it should be noted that the \textit{right-left} pattern is quite simple (either the right motor is turned fully on OR the left motor is turned fully on), which yields very fast reaction times. However, the information that can be delivered through this pattern is limited in comparison to the other patterns. One would need to combine the \textit{right-left} pattern with something else, say, the \textit{varying intensity} or the \textit{intervals}, to be able to deliver more complex information.

\subsubsection{Accuracy}
When looking at the number of correct answers, two vibration patterns stand out to be near perfect. As seen in Figure \ref{fig:LoggingOfCorrectButtonPress}, there are almost no errors in pressing the correct button in the \textit{right-left} pattern and the \textit{interval} pattern. This is interesting, because the same two patterns have the fastest reactions times as well. It should be noted that the \textit{right-left} pattern can only deliver binary information, while the \textit{interval} pattern in theory can deliver as much information as needed by increasing the number of intervals, e.g.\ having seven repetitions instead of four (within the limits of human working memory \citep{humanWorkingMemory}).

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/LoggingOfCorrectButtonPress}
\caption{Number of correct button presses for each of the patterns. The more towards 1 on the scale, the more correct presses.}
\label{fig:LoggingOfCorrectButtonPress}
\end{figure}

In the questionnaire, the test participants were asked: \textit{How experienced are you with using a traditional game controller?} The scale went from 1 (\textit{Not at all experienced}) to 7 (\textit{Very experienced}). When comparing this data with the reaction times (Figure \ref{fig:ExperienceAndReactionTimes}), there appears to be a relationship between the participants' self-proclaimed experience and their reaction times. In general, the more experience they had, the faster their reaction times were. Only the \textit{interval} pattern seems to be fairly consistent, while the \textit{right-left pattern} has a bell shape with the two extremes (experience level 1 and 7) being almost identical.

The biggest jump appears to be the \textit{static intensity} pattern, which is fairly consistent throughout most of the experience levels, but at level 7 it takes a big dip, going from +0.5 seconds to -0.1 seconds. That being said, in average it has a reaction time of 0.57 seconds.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/ExpWithController_ImpactingReactionTime_InDifferentVibrations}
\caption{The participants answered how much experience they had with a traditional game controller (TGC) on a scale from 1-7.}
\label{fig:ExperienceAndReactionTimes}
\end{figure}

\subsubsection{Secrecy and Distractions}
To investigate if the vibrations were concealed, so that the participants weren't aware or distracted by each other's vibrations, they were asked to rate themselves via two statements: \textit{I was aware of the other test participants' vibrations} and \textit{I was distracted by other test participants' vibrations}. Figure \ref{fig:PerceptionOfSecrecyAndNoise} shows two bars for each vibration pattern. The blue bars show the test participants' average awareness of the others' vibrations, and the green bars show their distraction levels. It appears that the test participants generally weren't concerned with each other's vibrations.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/PerceptionOfSecrecy&Noise}
\caption{The test participants' perception of how aware and distracted they were of other test participants' vibrations. Blue shows how aware they were, green shows how distracted they felt. High values mean more awareness/distraction.}
\label{fig:PerceptionOfSecrecyAndNoise}
\end{figure}

\subsubsection{Performance} \label{Performance}
For measuring the speed of the vibrations, the test participants were asked for their opinion on the statement: \textit{I felt like my reaction time was fast}. The results are shown in Figure \ref{fig:PerceptionOfSpeed}. Their perception of speed correlates well with how they actually performed, as shown in Figure \ref{fig:ReactionTimeMinusRumbleDuration}. The \textit{right-left} and \textit{interval} patterns appear to have the fastest reaction times, while the \textit{morse code} and \textit{varying intensity} patterns seem have the slowest%. Note that the data presented in the two figures are opposite to each other.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.80\textwidth]{Pictures/Design/PerceptionOfSpeed}
\caption{The test participants' perception of how quick their reaction times were.}
\label{fig:PerceptionOfSpeed}
\end{figure}

To determine the perceived difficulty of each vibration pattern, the test participants were asked to grade themselves on the statement \textit{I think it was easy to understand this vibration type}. Figure \ref{fig:PerceptionOfDifficulty} shows that the two easiest were the \textit{right-left} and \textit{interval} patterns, whereas the \textit{static intensity}, \textit{varying intensity} and \textit{morse code} patterns all were perceived to be relatively difficult.

When comparing the data from Figure \ref{fig:PerceptionOfDifficulty} to Figure \ref{fig:LoggingOfCorrectButtonPress} and Figure \ref{fig:ReactionTimeMinusRumbleDuration}, a correlation can be seen, as they all show that the \textit{right-left} and \textit{interval} patterns are the quickest, easiest, and have the highest percentage of correct button presses. On the contrary, the \textit{varying intensity} and \textit{morse code} patterns are consistently being positioned in the other end of the scale, i.e.\ being slower and more difficult.

To see how the test participants felt about the complexity of the vibration patterns, they were asked to rate themselves on the statement \textit{I felt like this vibration type can be used to deliver complex information}. Figure \ref{fig:PerceptionOfComplexity} shows unexpected results, as the \textit{right-left} and \textit{interval} patterns are perceived as the most complex, even though they are the two containing the least information and possess the highest number of correct button presses (Figure \ref{fig:LoggingOfCorrectButtonPress}) and have the quickest reaction times (Figure \ref{fig:ReactionTimeMinusRumbleDuration}).

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/PerceptionOfDifficulty}
\caption{Perceived difficulty of the vibration patterns.}
\label{fig:PerceptionOfDifficulty}
\end{figure}

Therefore, one could imagine that the test participants might have misunderstood the question about complexity. A possible explanation could be that the participants thought that it would be possible to combine multiple vibration patterns to deliver more complex information, e.g.\ by combining the \textit{right-left} pattern with the \textit{varying intensity} pattern.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.70\textwidth]{Pictures/Design/PerceptionOfComplexity}
\caption{The test participants' perception of how complex the different vibration types were.}
\label{fig:PerceptionOfComplexity}
\end{figure}
 
%!!!!!! \textbf{CONCLUSION OF COMPLEXITY} !!!!!!